Home › UP Board Class 10 › Mathematics › The figure shows several right triangles sharing…
The figure shows several right triangles sharing the same angle $A$. What does this illustrate about trigonometric ratios of a fixed acute angle? 
AThey change if the triangle becomes larger
BThey depend only on the hypotenuse
CThey remain the same for all similar right triangles with that angle
DThey are defined only for one particular triangle
Answer & Solution
Correct answer: C. They remain the same for all similar right triangles with that angle
The triangles formed are similar because they all contain the same acute angle $A$ and a right angle. In similar triangles, corresponding sides are proportional, so ratios such as $\sin A$, $\cos A$, and $\tan A$ remain unchanged. Thus trigonometric ratios depend on the angle, not on the overall size of the triangle.
Related questions
What is the derivative of $x^x$ for $x>0$?If $y=x^{\tan^{-1}x}$, then $\dfrac{dy}{dx}$ equalsThe derivative of $ in^{-1}x$ isThe derivative of $\cos^{-1}x$ isWhat is $\dfrac{d}{dx}(\tan^{-1}x)$?If $y=\dfrac{1}{x^n}$, then $\dfrac{dy}{dx}$ isWhich identity is correct?For the expression $ qrt{1-x^2}$, a useful trigonometric substitution is